Staff Working Paper ERSD-2012-06 Date: March 2012 World Trade Organization Economic Research and Statistics Division Self-Confirming Immigration Policy Paolo E. Giordani LUISS "Guido Carli" University Michele Ruta World Trade Organization Manuscript date: March 2012 Disclaimer: This is a working paper, and hence it represents research in progress. This paper represents the opinions of the author(s), and is the product of professional research. It is not meant to represent the position or opinions of the WTO or its Members, nor the official position of any staff members. Any errors are the fault of the author(s). Copies of working papers can be requested from the divisional secretariat by writing to: Economic Research and Statistics Division, World Trade Organization, Rue de Lausanne 154, CH 1211 Geneva 21, Switzerland. Please request papers by number and title.
Self-Confirming Immigration Policy Paolo E. Giordani y LUISS "Guido Carli" University Michele Ruta z World Trade Organization March 2012 Abstract We study immigration policy in a small receiving economy under self-selection of migrants. We show that a non-discriminatory immigration policy choice a ects and is a ected by the migratory decisions of skilled and unskilled foreign workers. From this interaction multiple equilibria may arise, which are driven by the natives expectations on the welfare e ects of immigration. In particular, pessimistic (optimistic) beliefs induce a country to impose higher (lower) barriers to immigration, which crowd out (crowd in) skilled migrants and thus con rm initial beliefs. This self-ful lling mechanism sustains the endogenous formation of an anti or pro-immigration prejudice. We discuss how the adoption of a skill-selective policy a ects this result. Keywords: Immigration policy, skilled/unskilled workers, small economy, multiple equilibria. JEL Classi cation: F22, J24, J61. This paper presents a new and more general model of our previous work that circulated with the title "Prejudice and Immigration". Disclaimer: The opinions expressed in this paper should be attributed to the authors. They are not meant to represent the positions or opinions of the WTO and its Members and are without prejudice to Members rights and obligations under the WTO. y Department of Economics and Finance, LUISS "Guido Carli" University, Viale Romania 32, 00197 Roma, Italy (e-mail: pgiordani@luiss.it). z Economics Research Division, World Trade Organization, Rue de Lausanne 154, 1211 Geneva, Switzerland (e-mail: michele.ruta@wto.org) 1
1 Introduction How are immigration and prejudice related? Three stylized facts in the empirical literature suggest that this relationship is a complex one. First, a deterioration of the skill composition of the migrant force is associated to stronger opposition to immigration and tighter restrictions in destination economies (Hanson et al., 2009, Facchini and Mayda, 2008 and 2009). Second, high-skill migrants are more internationally mobile than low-skill migrants and, hence, more responsive to changes in immigration policy in receiving countries (Belot anatton, 2008, McKenzie and Rapoport, 2010, Grogger ananson, 2011). 1 Third, skillselective immigration policies, that have been the exception rather than the rule in destination economies over the past two centuries, tend to be associated to more positive attitudes of natives over immigration and a less restrictive policy stance (Hatton and Williamson, 2004 and 2005, O Rourke and Sinnott, 2006). In this paper, we build a formal model of immigration that allows us to discuss the relationship between natives beliefs on the e ects of immigration (i.e. their prejudice, in the etymological sense of "pre" "judgement" or "preconceived opinion", whether positive or negative) and immigration policy in destination countries. While we provide further details below, the intuition of our argument can be simply stated. The skill composition of the migrant labor force a ects the welfare of a receiving society and, hence, its choice of migratory restrictions. This choice, in turn, a ects the quality of the migrant population as it alters the migratory decision of skilled and unskilled foreign workers. From this mutual interaction multiple equilibria may arise if receiving governments adopt non-discriminatory immigration policies. 2 Speci cally, if society has a belief that immigration will have a negative impact on welfare (anti-immigration prejudice), its government will choose high restrictions to the entry of foreign workers. In equilibrium, strict immigration policies that are not skill selective reduce the number of high-skill migrants (for reasons which will soon be clari ed), in which case immigration will be relatively more costly and social beliefs will be self-ful lled. 1 Speci cally, these authors nd that the choice of low-skill migrants is more constrained relative to high-skill migrants by such factors as geographical distance, cultural distance, colonial origin, network e ects (because of more stringent poverty constraints or lower adaptation capacity to diversity). The evidence on the actual distribution of foreign born workers in OECD countries shows that unskilled migrants concentrate in fewer destinations relative to the skilled (Docquier et al., 2008). 2 As discussed in more detail in the paper, we focus on the concept of self-con rming equilibria developed by Fudenberg and Levine (1993a). If 2
instead society has a belief that immigration will be bene cial (pro-immigration prejudice), it will set low restrictions, thus increasing the number of high-skill migrants and making this belief self-con rmed as well. Our analysis begins with a model of immigration with a sending and a receiving country. This is a useful benchmark and corresponds to the standard two-country structure of most immigration policy models (see the discussion on related literature below). The sending economy is populated by - skilled and unskilled - workers, who decide whether to migrate or not. The receiving economy chooses migratory restrictions to maximize the welfare of natives. The model has two key features. The rst is that both migration choices and migration policy are endogenous. The former depend on the economic incentives that foreign workers face, and on the policy regulating migratory ows enacted in the receiving country. Immigration policy in our set-up is parametrized by a cost borne by (high and low-skill) immigrants once in the destination country. The second important feature of the model is the assumption that low-skill and high-skill migrants a ect natives welfare di erently, the latter group being more bene cial to the receiving economy. 3 non-discriminatory optimal immigration policy for the host country. In this simple framework, we characterize the The benchmark model neglects a salient feature of migratory choices discussed above. Foreign workers choose not only whether to migrate or not but also, to a certain extent, which country to move to. In addition, as we have already claimed above, high-skill and lowskill migrants are not equally free in making this choice. We, therefore, extend the benchmark model in order to capture this key empirical feature. Speci cally, we assume that the sending and receiving countries are, respectively, part of larger origin and destination regions. The receiving country is a small economy which shares the same fundamentals with the rest of the destination region and can decide independently its immigration policy, without a ecting the rest of the region. We capture the higher international mobility of high-skill migrants by assuming that they can choose to emigrate to a larger set of destination countries relative to unskilled migrants. In this setting, non-discriminatory immigration policies have a novel e ect on the composition of the migrant labor force that could not emerge in the simple 3 Several theoretical arguments suggest that "skilled" migrants are more bene cial to the receiving country than "unskilled" migrants. These include: higher production complementarities between skilled labor and capital, greater exibility of the skilled labor market, higher scal cost of low-skill migrants. Borjas (1995) provides an overview of these arguments. 3
benchmark model. In particular, a restrictive immigration policy in the small destination country will reduce the number of high-skill workers, as they will choose to migrate where restrictions are lower (crowding out e ect). In contrast, a soft immigration policy will increase the number of high-skill migrants, in that it will attract them from the rest of the region (crowding in e ect). This mechanism is at the root of the key result of this paper on the relationship between prejudice and immigration. We prove that, when only non-discriminatory measures are available and a small economy in the receiving world decides immigration policy independently from the rest of the region, multiple equilibria arise which depend on the country s expectations. In the rst equilibrium, the economy bene ts of a high-skill immigration boom which is driven by optimistic expectations on the number of high-skill migrants. If a relatively large number of highly skilled foreign workers is expected to enter, the policy maker will rationally set low restrictions to immigration. The e ect of low barriers to immigration will be to attract -highly mobile- skilled migrants (crowding in e ect) and, hence, to validate initial beliefs. In the second (and opposite) equilibrium, the small economy can be stuck in an unskilled immigration trap, driven by pessimistic expectations. In particular, suppose that the host society has pessimistic beliefs about the quality of immigration. The rational response to this belief would be to impose higher barriers to immigration than the rest of the region. Given the skilled migrants freedom of choice, this policy will have the e ect of crowding them out. The composition of immigration in this country will then be biased towards low-skill immigrants, thus validating the initial pessimistic belief. We show that welfare is lowest for the receiving country under the "unskilled immigration trap" and highest under the "high-skill immigration boom". A key insight follows from this analysis which is radically di erent from the simple twocountry model of immigration. The self-ful lling mechanism described above may sustain the endogenous formation of a prejudice pro or against immigration. Given the nature of the equilibrium, these prejudices will be di cult to change and, therefore, even small di erences in initial perceptions may induce large and persistent di erences in immigration policy and outcomes across countries. In particular, our analysis raises the theoretical possibility that the hostility against immigrants may have resulted from a combination of pessimistic expectations and the non-selective barriers to immigration historically adopted by most receiving countries. This is complementary to explanations that emphasize the role of "fundamentals", such as 4
the size of redistributive programs or the substitutability between natives and migrants in labor markets, as determinants of public perceptions of immigration. What if receiving governments can adopt skill-selective policies? We argue that the multiplicity of equilibria disappears if the government introduces a fully discriminatory immigration policy that selects for the skills of foreign workers. Intuitively, a skill-selective policy that allows receiving countries to directly choose the composition of the migrant labor force would disprove prejudices in equilibrium. 4 This is important for three reasons. First, while (as noticed by Hatton and Williamson, 2005) family reuni cation still constitutes a major plank of immigration policy for permanent immigrants, policies that select for the skills of foreign workers are becoming empirically more relevant in recent years, as a growing number of receiving countries are changing their rules on immigration (e.g. the new rules on the Blue Card in the European Union). Second, we argue that the extensive and protracted use of nondiscriminatory policies adopted in most host economies in the past two centuries is essential to understand the self-ful lling nature of immigration policy and the endogenous formation and persistence of natives prejudices. Third, and more importantly, this nding points to a novel (and positive) e ect of skill-selective policies on destination countries. A switch to a discriminatory policy improves the quality of migrants and the attitudes of natives towards immigration and, ultimately, may contribute to eradicate a pre-existing anti-immigration prejudice. This paper contributes to the growing economic literature on formal models of immigration policy (among others, Borjas, 1995, Benhabib, 1996, de Melo et al., 2001, Dolmas and Hu man, 2004, Ortega, 2005, and Facchini and Willman, 2005). Di erently from the present study, these works assume a two-country structure and consider as exogenous the migratory decision of foreign workers. Bellettini and Berti Ceroni (2007) and Bianchi (forthcoming) focus on the interdependence between immigration policy in the host economy and immigration decisions, but di erently from our analysis they also abstract from the location decision of foreign workers. Two recent contributions by Bubb et al. (forthcoming) and Giordani and Ruta (2011) are closely related to this paper. They remove the two-country assumption of 4 However, as we discuss in Subsection 3.5, there are limits to the ability of governments to set discriminatory immigration policies. In particular, there is a distinction between border measures, which can be skill-selective, and behind-the-border measures that can often only be set on a non-discriminatory basis. Hence, fully skillselective and non-discriminatory policies are best seen as the extremes of the spectrum of immigration policies that receiving governments can adopt in practice. 5
most formal immigration policy models and nd that multiplicity of equilibria can characterize immigration policy. Aside from focusing on the case of a small economy rather than emphasizing the interaction of large countries, this paper di ers from previous contributions as it allows for the di erent international mobility of high and low-skill migrants. It is this novel feature that determines the endogenous formation of an immigration prejudice. The rest of the paper is organized as follows. In the next section we introduce the benchmark model, analyze the migration choice of skilled and unskilled foreign workers and characterize the optimal immigration policy for the receiving country. In Section 3 we extend the model to consider a small receiving economy, analyze the new migration choice, and derive the policy equilibria for this economy. Section 4 analyzes a speci c model of immigration policy for illustrative purposes. Concluding remarks are in Section 5, while all proofs are in the technical appendix. 2 A Benchmark Model of Immigration Policy We begin with a simple two-country structure as a useful benchmark. The world is made up of a receiving country, or "home" (H), and a sending country, "foreign" (F ). Two key sets of actors characterize the economy: foreign workers, who choose whether to migrate or not to H; and the home government, which decides immigration policy to maximize natives welfare. Country F is populated by measures F s and F u of, respectively, skilled and unskilled workers. Country H s welfare depends on the number and the quality of immigrants. Denote by I s and I u the (endogenous) measure of skilled and unskilled immigrants to H and de ne H s welfare as a twice continuously di erentiable function in its two arguments, W H (I s ; I u ). We assume that @W H =@I s > 0 8I s 2 [0; F s ], i.e. skilled migrants are always bene cial to the host economy, and @W H =@I u 7 0, meaning that unskilled immigration may improve or lower natives welfare. To make the problem economically interesting, assume that, after a certain threshold, unskilled migrants become harmful for the receiving economy, that is: 9 I u 2 (0; F u ) such that @W H =@I u < 0 for any I u 2 I u ; F u. 5 5 Section 4 presents a speci c model where the di erential welfare e ect of low-skill immigration is rooted in its higher scal cost in presence of redistributive policies in the host economy. As discussed in the Introduction and shown below, the origin of this di erential e ect on natives welfare is immaterial for the results of this paper. 6
2.1 The Migration Choice Migration is assumed to be a one-time and non-reversible decision. Each immigrant i - whether skilled or unskilled - faces a psychological cost to leave her own country, i, measured in migrants utils and uniformly distributed in [0; 1]. In addition, the government in H can set up an immigration policy which is parametrized by a cost -still measured in terms of utilsborne by immigrants once in the new country, H 2 R +. One can interpret H in several ways, from the number of bureaucratic procedures (i.e. the time a worker needs to spend applying for a work permit in the receiving country, which implies an opportunity cost for the applicant), to laws that a ect the life of immigrants in the host country, such as the number of years to obtain voting rights or citizenship. This policy is assumed to be non-discriminatory, while the case of a skill-selective immigration policy is analyzed in Subsection 3.5. De ne the two continuously di erentiable functions, b s ( H ; z) ; b u ( H ; z), as the net bene ts from migrating to H for, respectively, skilled and unskilled migrants. It is natural to suppose that @b j =@ H < 0 for j = s; u, that is, a more restrictive policy lowers the bene ts from migrating. The variable z instead captures all other factors which may a ect the decision to migrate, such as the wage di erential between H and F or the presence of a social redistributive policy in country H (Section 4 provides an example where these aspects a ect the decision to migrate). An unskilled foreign worker i will migrate to H if and only if while a skilled foreign worker i will migrate to H if and only if b u ( H ; z) i ; (1) b s ( H ; z) i : (2) We can then nd the two threshold values of, call them u and s respectively for unskilled and skilled, such that all those below that value are willing to migrate. We have u = b u ( H ; z) and s = b s ( H ; z). All unskilled workers whose is lower than u, and all skilled workers whose is lower than s are willing to migrate. If both unskilled and skilled foreign workers are distributed 7
uniformly in [0; 1], the number of unskilled and skilled migrants will be respectively I u = u ( H ; z) F u and I s = s ( H ; z) F s : (3) A higher H lowers the bene ts from migrating and, hence, lowers the number of both unskilled and skilled migrants. 2.2 The Optimal Immigration Policy at Home We now determine the optimal (non-discriminatory) immigration policy for the receiving country. The problem for the home government is the one of nding the value of H which maximizes the welfare function, W H ( u ( H ) F u ; s ( H ) F s ), where we have substituted for the number of unskilled and skilled migrants given in (3). 6 De ne ^ arg max H W H ( u ( H ) F u ; s ( H ) F s ) ; as the optimal immigration policy. Formally, assuming for simplicity that the welfare function is strictly concave in H, policy ^ is the one solving the rst order condition @W H @I u @I u @ H + @W H @I s @I s @ H = 0; that is, the one for which the marginal bene ts from a policy tightening (in terms of fewer unskilled migrants, (@W H =@I u )(@I u =@ H ) > 0) exactly equalizes its marginal costs (in terms of fewer skilled migrants, (@W H =@I s ) (@I s =@ H ) < 0). 7 The next section shows that, once we move away from the simple two-country structure of the benchmark model, expectations (and not only fundamentals) play a role in immigration policy, and that this leads to a multiplicity of equilibria. 3 Immigration Policy in a Small Economy Most models of immigration policy have a two-country structure, as the one discussed in the previous section. However, as emphasized in the introduction, this structure fails to consider 6 To ease notation we have dropped the catch-all, exogenous, variable z. 7 Needless to say, we can exclude that the optimal policy be associated with a number of unskilled migrants lower than I u. 8
two relevant features of migratory choices. First, a model with only one receiving country inevitably neglects that some foreign workers may not only decide whether to migrate or not, but also select their destination country. Secondly, low-skill migrants are generally more constrained in their choice as to where to migrate compared to high-skill migrants. We now develop an extension of the model above to incorporate these two aspects. Consider country H and country F as part of, respectively, a large receiving region (R) and a large sending region (S). Countries H and F are identical to the regions they belong to, but are assumed to be small compared to them (so that changes in these countries do not a ect the rest of the regions). We can easily capture this structure by imagining that H and F are two zero-mass countries in two intervals [0; 1], representing the measures of both receiving and sending regions. As the evidence provided in the introduction suggests, skilled foreign workers are more internationally mobile relative to low-skill foreign workers as they have more freedom in choosing their destination country. We capture this empirical nding with the simplest possible set of assumptions. First, we suppose that low skill foreign workers are fully constrained in their location decisions, so that those potentially entering into country H are still F u. Second, the pool of skilled foreign workers targeting country H is made up of two subsets. A rst group of size F s (where 0 < 1) is constrained to migrating to country H. A second group of size F s (where > 1) is "free" to target country H as well as any other country in the rest of region R. This construction captures the simple idea that skilled foreign workers potentially entering into country H are no longer F s in a world where high-skill migrants have some degree of freedom in choosing the country of destination. 8 Country H selects immigration policy H independently. We focus on the equilibrium characterization of country H while supposing that the rest of the receiving region implements the optimal immigration policy. Since country H is simply a "scaled down" version of region R, it must be R = ^. We characterize the mutual interaction between the policy maker in country H and foreign workers as a two-stage sequential game in which (i) the former chooses 8 Note that this formalization could be generalized in several directions. For instance, and more realistically, one could think that each foreign worker, whether skilled or unskilled, has a favorite destination country and a distribution of "switching costs", that is, of costs associated to migrating somewhere else. Each foreign worker could then in principle migrate everywhere inside the region R, but the cost would vary with the destination. Taking this route would complicate our framework but would not alter substantially any of our results, as long as these switching costs (inversely capturing the exibility over choice of destination) are assumed lower for high-skill than for low-skill migrants (which is what the empirical evidence suggests). 9
immigration policy as a function of the expected migratory in ows, (ii) the latter make their migratory choices depending on this immigration policy. To nd the policy equilibria in country H, we analyze the behavior of the policy maker and that of foreign workers as described in points (i) and (ii), starting with the latter. 3.1 The New Migration Choice The migration choice of low-skill foreign workers is identical to that developed in the benchmark model. These workers migrate to H if and only if (1) holds, from which the number of unskilled migrants, as a function of the country H s immigration policy, is again given by I u = u ( H ) F u. High-skill foreign workers targeting country H compare their pay-o as immigrants in country H to the one from their country of origin, and migrate if (2) holds. The number of constrained skilled migrants will then simply be s ( H ) F s. The subset of free skilled workers, however - F s - also compare their pay-o in H with the one they would obtain in region R, and choose country H if the former is higher than the latter. formally, More b s ( H ) i > b s (^) i (4) () H < ^: The relation above holds because it is db s = < 0. All free skilled workers whose psychological cost is lower than s will enter country H if and only if H < ^ (crowding in), while they will migrate to the rest of the region if and only if H > ^ (crowding out). When H = ^, these workers will be indi erent between country H and the rest of the region R, and we assume that in this case they will distribute uniformly across the receiving region. The total number of skilled migrants, as a function of immigration restrictions in H, will then be I s = s ( H ) F s H where 10
H = 8 >< >: if H < ^ 1 if H = ^ if H > ^. (5) INSERT FIGURE 1 ABOUT HERE The sum of skilled and unskilled immigrants, s ( H ) F s H + u ( H ) F u, is a piecewise continuous function in H whose only discontinuity point is H = ^. It can be interpreted as the immigrants best-response function, as it captures the optimal reaction of immigrants to any level of immigration restrictions chosen by the policy maker in H. What makes this behavior interesting, and di erent from the one we have illustrated in the benchmark model, is the step function H ( H ) (de ned in expression (5) and depicted in Figure 1), which captures the pool of high-skill foreign workers targeting country H as a function of migratory restrictions enacted in that country. This function is responsible for the discontinuity of the immigrants best-response to immigration restrictions at point H = ^. 3.2 The Immigration Policy Choice We have seen above that the migration choice of foreign workers depends on the immigration policy enacted in country H. In particular, internationally mobile skilled workers might decide not to target country H when observing a comparatively stricter policy than in the rest of the region and vice-versa. In this subsection we analyze how immigration policy in country H depends on the expected migratory behavior of foreign workers, and prove an "instrumental" result, which we are going to use in the next subsection. As in the two-country model, the policy maker in the small economy H chooses immigration policy to achieve the combination of skilled and unskilled migration which maximizes natives welfare, W H (I u ; I s ). The crucial di erence with respect to the policy problem illustrated in Section 2 is that here the migratory restrictions chosen by country H to reach that combination, H (), also depend on H, that is, on the pool of high-skill foreign workers that the policy maker expects will target H. 9 Denoting the welfare function as 9 Notice that the expected and actual number of free skilled foreign workers targeting H are both denoted by H. Clearly, in equilibrium, they coincide. 11
W H ( H ; H) W H ( u ( H ) F u ; s ( H ) F s H), we de ne H ( H) arg max fw H ( H ; H)g as the optimal immigration policy as a function of H. The relationship between H and H is analyzed in the following Lemma 1. The optimal (non-discriminatory) immigration policy in country H, H (), is a decreasing function of H 2 ;. INSERT FIGURE 2 ABOUT HERE The intuition for this result is straightforward. The higher the expected pool of skilled foreign workers ( H), the higher the marginal costs associated to a tightening of immigration policy, and the lower the optimal migratory restrictions. The curve drawn in Figure 2 describes the locus of points in which immigration policy in country H is optimal for any value of H between and. Clearly, when H = 1, the maximum problem coincides with the one analyzed in Subsection 2.2, and hence H ( H = 1) = ^. A decrease in the expected pool of skilled foreign workers ( H #) is associated with a tightening of immigration policy ( H "), and vice-versa. Hence, Lemma 1 implies that H ( ) > H (1) > H, as < 1 <. 3.3 Self-Con rming Policy Equilibria In this subsection, we study the non-discriminatory equilibrium immigration policy. We focus on self-con rming equilibria à la Fudenberg-Levine (1993a). 10 For country H, an equilibrium is de ned as a con guration in which (i) the policy maker chooses the immigration policy which maximizes her objective function given her (correct) beliefs on the migratory in ows, (ii) foreign workers make their migration choice to maximize their utility for given immigration policy ( H ). Our results are summarized in the following Proposition 2. Three policy equilibria exist in country H: 1. The "high-skill boom" equilibrium, where the non-discriminatory policy in H is softer, H soft < ^, and the 10 The self-con rming equilibrium has recently found several applications in the macroeconomic literature, including Sargent et al. (2006) theory of in ation and Alesina and Angeletos (2005) model of fairness and redistribution. For a concise review of macroeconomic applications of this concept refer to Fudenberg and Levine (2009). 12
proportion of skilled migrants over native workforce as well as welfare are higher than in the rest of the receiving region R (crowding in). 2. The "globally optimal policy" equilibrium, in which the policy H (1) = ^, the proportion of skilled migrants over native workforce as well as welfare are equal to those in R. 3. The "unskilled migration trap" equilibrium, in which the non-discriminatory policy in H is tighter, H ( ) tight > ^, and the proportion of skilled migrants over native workforce as well as welfare are lower in country H than in the rest of the receiving region (crowding out). A graphical intuition of this result is provided in Figure 3, where the two schedules, capturing the pool of high-skill foreign workers and the optimal immigration policy, intersect in three points, which constitute the policy equilibria of country H. INSERT FIGURE 3 ABOUT HERE In this model, expectations are self-ful lling. In a country where the dominant belief is that few skilled migrants will enter, the government sets a restrictive immigration policy. A restrictive policy, in turn, "scares" at least some skilled foreign workers who prefer to migrate to other countries in the region. This creates a trap with few skilled migrants in H and lower welfare compared to the rest of the receiving region. The opposite -i.e. good- equilibrium with high skilled immigration and higher welfare is triggered by a positive belief on high skilled immigration (and its welfare e ects). Finally, the third possibility is that a country expects the same proportion of high-skill migrants over native population as in the rest of the region. In this case, the equilibrium implies that the policy and the welfare in country H are exactly as in region R, and beliefs are again vindicated. A Cournot tatonnement argument suggests that the "high-skill boom" and the "unskilled trap" are locally stable equilibria, while the "globally optimal policy" equilibrium is unstable. The very existence of the latter indeed, crucially hinges on an assumption "disciplining" the number of high-skill migrants when H = ^. Under that policy, high-skill migrants are indi erent as to where to migrate. For reasons of symmetric migratory behavior across the receiving region, we have found it reasonable to assume that H = 1. If that were not the case, however, the equilibrium would disappear. Moreover, a small perturbation of 13
this behavior makes the economy diverge towards either of the two equilibria (depending on whether that perturbation is positive or negative). Consider a perturbation of H = 1, for a however small real number. If > 0, for Lemma 1 the government reacts by slightly softening its immigration policy, that is, H (1 + ) < ^. Skilled migrants respond to this policy by crowding in country H, which in turn leads the policy maker to set up H = soft. The economy then converges to the high-skill boom equilibrium. Conversely, if < 0 the government sets up a slightly tighter immigration policy. As a consequence, skilled migrants crowd out of country H, the policy maker sets up H = tight, and the economy converges to the unskilled migration trap. This sequential discrete tatonnement process is captured graphically in Figure 4. INSERT FIGURE 4 ABOUT HERE Finally note that our extension has brought about rather di erent results from the baseline model. First, the globally optimal policy equilibrium, which is the only equilibrium of the benchmark model, is unstable, and its existence crucially hinges on the assumption of complete symmetry. Secondly, two new policy equilibria emerge, the high-skill boom and the unskilled migration trap. As discussed in the next subsection, these equilibria respectively rationalize the formation of a pro- and an anti-immigration prejudice. A situation that could never materialize in the benchmark model of immigration policy. 3.4 Endogenous Immigration Prejudices This subsection provides an interpretation of the self-con rming immigration policy equilibria. In a self-con rming equilibrium each player plays her best response to her beliefs on the opponent s behavior, and beliefs must be correct along the equilibrium path. The peculiarity of this equilibrium is that it is in fact compatible with incorrect beliefs o the equilibrium path, also called "superstitions". The self-con rming equilibrium is a generalization of the Nash equilibrium, whose rationale can be brie y explained as follows. If it is true that "non-cooperative equilibria should be interpreted as the outcome of a learning process, in which players revise their beliefs using their observations of previous play" (Fudenberg-Levine, 1993a, p. 523), the concept of self-con rming equilibrium captures the idea that players tend 14
to learn - and hence to have correct beliefs on - their opponents behavior along the path followed by the equilibrium but not (necessarily) in contingencies that are in fact never played. If we follow this logic, the "anti-immigration prejudice" may be interpreted as the social (or the policy maker s) conviction that the pool of skilled foreign workers potentially entering country H simply be F s. This conviction in fact contains a "superstition" (namely, an o -the-equilibrium incorrect belief), that when the policy maker sets up a soft immigration policy, the pool of high-skill foreign workers will still be F s. Indeed, that is not the case, since the size of the pool is disciplined by (5). The policy maker of a country that is stuck in an unskilled migration trap, however, ignores it, and the reason is that she never observes it. The only thing she observes is what happens along the equilibrium path, where the pool of high-skill foreign workers is F s. In other words, no evidence ever emerges that contradicts the policy maker s belief, which can in principle be sustained forever to the extent that play follows the equilibrium path. An analogous interpretation could be given to the "pro-immigration prejudice". Driven by the optimistic belief that most skilled foreign workers will target country H (F s ), the policy maker sets up a soft policy which will in fact attract most skilled immigrants. Notice, however, that this is not the only possible interpretation of the high-skill boom equilibrium. In fact, this solution does not need any o -the-equilibrium "superstition" and can be sustained as a subgame-perfect equilibrium. One might argue that a society that is stuck into the unskilled migration trap might experiment alternative paths and eventually learn its mistake. As argued by Fudenberg and Levine (1993b), superstitions may vanish if players are patient enough to carry out a su cient amount of experimentation o the equilibrium. In our theoretical framework, deviating from the restrictive policy could in principle help the policy maker learn the migratory behavior of free skilled foreign workers (as captured by (5)), and thus eradicate the superstition. Notice, however, that a "timid" reduction of migratory restrictions would not be su cient to reach this goal. As is apparent from Figure 5, along the unskilled migration trap the policy maker -implementing policy tight - always observes HF s = F s, and any "experimentation" in the whole "policy region" between tight and ^ would not bring any evidence of H 6=. In other words, unless the policy maker opens up migration policy at or above ^, she will never observe any change in the pool of skilled foreign workers targeting H. Under the 15
principle that "you learn what you observe", the policy maker would then need to soften "remarkably" her immigration policy to be able to learn her mistake. This sizeable shift in immigration policy might not be easy to attain, especially when observing that in the real world (i) high-skill foreign workers do not respond instantaneously to changes in immigration policy, which may render the real learning process far more complex and slow than suggested in our simple stylized world, (ii) patience may not be a major virtue of policy makers who, along the unskilled migration trap, must respond to the voters hostility towards immigration (Facchini and Mayda, 2008). 3.5 Skill-Selective Policies We now discuss the case of a discriminatory immigration policy and argue that a policy that can perfectly discriminate among foreign workers with di erent skills removes the multiplicity of equilibria for the small economy. 11 Given that high-skill foreign workers are bene cial to country H, the best immigration policy for this skill group (^ s H ) is an "open door" policy (say ^ s H = 0, if we do not consider the possibility of subsidizing immigration). Low-skill migrants are instead bene cial only up to a certain threshold (that we denoted by I u ), beyond which they become harmful for the receiving economy. The optimal policy for lowskill migrants (^ u H ) is then implicitly de ned by equation I u = u (^ u H ) F u. This optimal pair of immigration policies, (^ s H ; ^u H ), is totally una ected by the policy-maker s beliefs on migratory ows. Finally, notice that social welfare in country H depends on whether or not the rest of the receiving world (region R) also implements a selective policy. In fact, if country H were the only country ltering skills, it would enjoy a higher number of skilled migrants (F s ) and a higher welfare with respect to region R. While discriminatory measures break the self-ful lling mechanism that we have highlighted above and thus eliminate the multiplicity of equilibria, it is important to re ect on what constitutes a skill-selective policy. Immigration policy, as de ned in Section 2, is a combination of border and behind-the-border measures that a ect the life of foreign workers in the host country. While border measures, as a point system, can in principle target differently high and low-skill migrants, there are important limitations to the extent to which behind-the-border measures can be set in a discriminatory fashion. For instance, the number 11 Formally, this result is trivial, which is why we omit the proof and provide only an intuitive discussion. 16
of years required to obtain citizenship can, and often do, vary for di erent skill groups of foreign workers. However, access to public health systems or to public education for migrants children are generally not o ered on a discriminatory basis for both e ciency and ethical reasons. This implies that fully discriminatory and non-discriminatory policies are best seen as the extreme of the spectrum of immigration policy that a country can adopt. Actual regulations will lie somewhere in between. In this context, introducing stronger lters for di erent skill groups at the border will moderate, but not necessarily eliminate, the self-con rming nature of immigration policy. 4 An Illustrative Example In this section we construct a model of immigration policy capturing a few salient features of receiving economies and of migratory decisions, and we illustrate the possibility of prejudices pro or against immigration arising in the receiving economies. 12 The structure of the world is identical to that introduced in Section 3. Country F is a small sending country, populated by F u unskilled and F s skilled workers and belonging to a large sending region, S. Country H is a small receiving country, populated by N H natives and K capitalists (each owning one unit of capital), and belonging to a large receiving region, R. The receiving small economy H produces competitively a unique nal good via a Cobb- Douglas technology in e ective labor (L) and in capital, denoted by K: Y = K L 1 : E ective labor is de ned as L N H + " ui u + " si s ; where " u and " s denote the productivities of unskilled and skilled foreign workers respectively, with " u < " s 1, and, as before, I u and I s denote the endogenous number of unskilled and skilled migrants. Each of the N H natives supplies inelastically one unit of labor, whose productivity is normalized to 1. Natives and migrants utility is linear in their (disposable) income, which is entirely spent to consume the only nal good produced in the economy 12 Our previous working paper (Giordani and Ruta, 2009), which has been superseded by this article, provides further details of this example. 17
(whose price is normalized to one). Factor demands for capital and labor per e ciency unit (r H, w H ) are given by their respective marginal productivities from the Cobb-Douglas technology above. Finally, country H has a social policy that redistributes resources from native capitalists to low-skill foreign workers. This policy consists of an exogenous and xed lump-sum transfer u to unskilled migrants which is nanced through a proportional tax 2 [0; 1] on the capitalists income. 13 The balanced budget constraint can be written as r H K ^ = u I u where I u is the endogenous number of unskilled migrants entering country H. We capture the greater freedom of choice of skilled migrants with respect to unskilled migrants exactly as in the model in Section 3. The pool of potential unskilled migrants to country H is F u : these workers either go to H or stay in their country of origin. The pool of potential skilled migrants to country H is instead F s (with > 1): a subset of them, F s, are constrained in their choice (they either go to H or stay in their country of origin). All others, Fs, are free to choose whether to move to H or any other country in the receiving region. In F the wage rate is exogenous and denoted by w. Moreover, and only for simplicity, suppose that foreign unskilled workers are unproductive (" u = 0), and hence that they migrate only to bene t from the social assistance program. 14 An unskilled foreign worker i will migrate to H if and only if u H i 0; where H and i are de ned as in Section 2. From the expression above, the number of unskilled migrants as a function of migratory restrictions can be obtained as u F u with u = u H. Given this number of unskilled migrants, the tax rate on capital (^) that balances the budget of the income support program is ^ = u ( u H ) F u r H K (6) 13 Naturally, one can model the social policy in the receiving country in a number of di erent ways (for instance, taxing native labor rather than capital). Alternative formalizations would generally not alter the logic of our results as long as the social policy implies a net transfer of resources from natives to unskilled foreign workers. 14 Nothing substantial would change if " u were strictly positive (but lower than " s). Algebra simpli es a lot with this hypothesis though. 18
Similarly, skilled foreign workers targeting country H compare their pay-o as immigrants in country H to the one from their country of origin, and migrate if w H " s H i w " s; from which the threshold s = (w H w ) " s H is determined. The number of constrained skilled migrants will then simply be s F s. The subset of free skilled workers, however - - also compare their pay-o in H with the one they would obtain in region R, F s and choose country H if the former is higher than the latter. Denoting by ^ the immigration policy set up in the rest of the receiving region, we have w H " s H i > ^w" s ^ i () H < ^; where ^w is the equilibrium wage in region R when R = ^. The relation above holds because, as we prove in Appendix B, a given policy change causes a smaller change in wage, that is, (" sw H ) = H < 1. Country H is then subject to a crowding out if H > ^ and to a crowding in if H < ^. As in the model of Section 3, the total number of skilled migrants, as a function of immigration restrictions in H, will be s F s H with H given in (5). Although very simple, this model is compatible with several well-established empirical results. First, the data con rm that high-skill migrants are highly responsive to wage earning di erences (Grogger ananson, 2011). Second, the idea that the generosity of the welfare system in destination countries serves as a magnet to unskilled migrants nds support in Boeri et al. (2002) and Cohen and Razin (2008) among others. De ne the welfare function of the government in the small receiving country as a weighted sum of the utilities of native capitalists and native workers: W H ( H ; H) a r H ( H ; H) K (1 ^) + (1 a) w H ( H ; H) N H ; (7) where the expression for ^ is given in (6), and where r H = [K= (N H + " si s )] 1, w H = (1 ) [K= (N H + " si s )], with I s = s F s H being the expected number of skilled foreign 19
workers. Immigration has clear redistributive e ects on the native population. In particular, the entry of foreign workers hurts native workers (by lowering their wage), and it has an ambiguous e ect on capitalists (in that it raises both their rent (r H ) and their tax rate (^)). The policy maker might not be neutral with respect to the distributional consequences of immigration, which is captured by the weight on the utility of capitalists, a 2 [0; 1]. 15 The policy maker maximizes condition (7) with respect to H. In Appendix B we prove that the (politically) optimal migratory restrictions in country H are a decreasing function of H: = < 0 8 H 2 ; (that is, the analogous to Lemma 1 for this economy). This, together with the migratory behavior of skilled foreign workers, implies that the strategic interaction between migrants and the policy-maker of country H is identical to that described in Section 3. It follows that Proposition 2 applies to this economy as a special case of the general model presented in this paper. 5 Conclusion This paper provides a model to investigate how attitudes towards immigration and immigration policy interact with migratory decisions. We have shown that in a setting where high skilled foreign workers are more bene cial and more mobile than unskilled migrants, di erent perceptions on immigration in host countries lead to radically di erent outcomes. Optimistic beliefs on immigration induce a government to set low restrictions which attract high-skill foreign workers, while pessimistic beliefs bring high restrictions which scare skilled immigrants. This self-ful lling mechanism sustains the endogenous formation of a prejudice, pro or anti immigration. While clearly not the only explanation, our work sheds some light on why di erences in attitudes towards immigration may be so rooted in di erent countries. This analysis contributes to the discussion on the proper design of immigration policy in host countries. The model implies that the choice of the right policy may have a signi cant impact in the short run, as well as in the long run through the formation of attitudes towards immigration that will change only slowly. First, the small economy setting helps us clarify that a country must be careful in implementing non-discriminatory restrictions to control 15 As it is well understood from the theory of collective action (Olson, 1965), governments tend to give higher weight to organized special interests. This may explain deviations from pure welfare maximization. Facchini et al. (forthcoming) nd evidence of the over-representation of capitalists interests in immigration policy in the US. 20
the migration ow. The reason is that immigration policies a ect not only the number of migrants but also their composition, and a restrictive policy could indirectly act as an instrument of selection of the lowest quality immigrants. Secondly, the economic literature has proposed several arguments in favor of policies that lter foreign workers in terms of observable skills. This paper adds to these arguments that selective policies may in uence natives attitude towards immigration and, hence, increase support for further reductions of barriers. In principle, an anti-immigration prejudice could be moderated via a combination of rules that favor more productive migrants with a more open immigration policy. 21
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